Semiclassical Motion from Quantum‐Mechanical Operators

Application of quantum‐mechanical kinetic energy operators to familiar wave‐functions reveals dynamic equations of motion that are strikingly classical in form. In particular, if the equations of motion arising from application of the method to hydrogen wave‐functions are considered as pertaining to Keplerian orbits, they give rise to semimajor axes identical to the Bohr radii and hence total energies and orbital frequencies the same as those for the Bohr atom. A particularly important feature of this method is that it is not just true for the limiting case of large n, but is apparently true for all n, including n = 0 and n = 1.